This invention relates generally to electrical impedance-matching circuits, and more particularly, it relates to a circuit for impedance matching an electrical signal-generating transducer to electrical signal-processing circuitry with minimum degradation of both the electrical signal and the signal-to-noise ratio.
A number of modern signal-processing systems utilize devices generally termed transducers in the collection, transformation, amplification or transmission of signals of various forms (e.g., electrical, optical, inertial, mechanical). For example, photodetector sensors in electronic video cameras, missile seekers and laser communication systems collect optical signals and transform them into electrical signals; inertial sensors such as accelerometers, gyros and gravity gradiometers in navigation systems collect inertial signals and transform then into electrical signals; and repeater amplifiers in computers and electrical, microwave and laser communication systems function to amplify an electrical signal without changing its form. The foregoing transducer types have the general characteristics that they couple to a source of signals (e.g., electrical, optical, inertial, mechanical, gravitational) and produce a replica of that signal with more or less fidelity. sometimes maintaining the same form of the signal (e.g., electrical-to-electrical, mechanical-to-mechanical), but often transforming the signal from one form to another (e.g., light-to-electrical, gravitational-to-electrical).
The objective of a transducer is to carry out the desired transformation without degradation of the signal, either by lowering its level or by adding noise, thus maintaining the signal-to-noise power ratio (SNR) of the system. Each of the aforementioned transducers, being subject to various non-ideal constraints, must of necessity introduce some noise, which becomes mixed with the signal. Although noise may sometimes be multiplicative or of a complex nature, the noise is usually random and additive. (Additive random noise is assumed for purposes of the following discussion.)
Each transducer also has associated with it an impedance. This impedance may be complex, but usually it is purely resistive or can be made so with the addition of properly matched reactive impedances. Irrespective of the nature of the impedance, it is the resistive portion of the transducer impedance that is of most concern, since it is the source of additive noise. Thus, at the output terminals of an electrical signal-generating transducer, a voltage exists consisting of both the desired signal voltage and a noise voltage, the noise voltage being that introduced by the transducer resistance. An effective signal-to-noise power ratio (SNR).sub.0 for the transducer may be defined as the ratio of the signal power (voltage squared) to the noise power (voltage squared) at the transducer output terminals.
It is well known in the electronics art that if it is desired to process the transducer output voltage with minimum degradation of the signal-to-noise power ratio, one should use signal-processing circuitry (such as an amplifier) with an input load resistance that is as high as possible, along with a bandwidth that matches the bandwidth of the transducer output signal.
The signal-to-noise power ratio, although important, is not the only concern in wideband signal-processing systems. If there is a substantial distance between the transducer and the following signal-processing stage (e.g. amplifier), then these components must be connected by a transmission line. If the signal is of very high frequency and the transmission line is long, then the wavelength of the signal becomes comparable to the transmission line length. In such cases, if the impedance of the transmission line is not matched to that of either the transducer or the following stage, reflected and standing waves can exist in the transmission line which result in undesirable distortion of the signal. Therefore, it is usually desirable to select the impedance of the transmission line to match the impedance of the transducer, and also, to choose the input load resistance of the following stage to match the transmission line impedance.
When a transducer, transmission line and following signal-processing stage are impedance-matched as described above, two penalities are paid at the input to the following stage. First, the signal amplitude decreases by a factor of two from its original value, and second, the signal-to-noise power ratio suffers a degradation of 3 dB.
In a paper by W. S. Percival, "An Electronically `Cold` Resistance", The Wireless Engineer, Vol. 16, (May 1939), pp. 237-240, it is pointed out that if a transmission line were terminated with a noiseless resistance, the signal-to-noise ratio is not altered. Thus, by terminating a transmission line with a properly matched low-noise resistance, the desired impedance matching may be achieved with minimum loss in the signal-to-noise ratio. Nevertheless, the signal applied to the stage following the transmission line is reduced to half of its original amplitude. As a result, additional amplification is required, adding to the cost and complexity of the system. In addition, if the following stage is not perfectly noise-free, then the signal-to-noise ratio is also degraded more than if the signal were maintained at its original amplitude.